Thermalisation
{{Short description|Tendency of bodies towards thermal equilibrium}}
{{Use British English|date=July 2021}}
In physics, thermalisation (or thermalization) is the process of physical bodies reaching thermal equilibrium through mutual interaction. In general, the natural tendency of a system is towards a state of equipartition of energy and uniform temperature that maximizes the system's entropy. Thermalisation, thermal equilibrium, and temperature are therefore important fundamental concepts within statistical physics, statistical mechanics, and thermodynamics; all of which are a basis for many other specific fields of scientific understanding and engineering application.
Examples of thermalisation include:
- the achievement of equilibrium in a plasma.{{Cite web|url=http://sdpha2.ucsd.edu/coll_therm.html|title=Collisions and Thermalization|website=sdphca.ucsd.edu|access-date=2018-05-14}}
- the process undergone by high-energy neutrons as they lose energy by collision with a moderator.{{Cite web|url=https://www.nrc.gov/reading-rm/basic-ref/glossary/thermalization.html|title=NRC: Glossary -- Thermalization|website=www.nrc.gov|language=en|access-date=2018-05-14}}
- the process of heat or phonon emission by charge carriers in a solar cell, after a photon that exceeds the semiconductor band gap energy is absorbed.{{Cite journal |last1=Andersson |first1=Olof |last2=Kemerink |first2=Martijn |date=December 2020 |title=Enhancing Open-Circuit Voltage in Gradient Organic Solar Cells by Rectifying Thermalization Losses |journal=Solar RRL |language=en |volume=4 |issue=12 |pages=2000400 |doi=10.1002/solr.202000400 |s2cid=226343918 |issn=2367-198X|doi-access=free }}
The hypothesis, foundational to most introductory textbooks treating quantum statistical mechanics,Sakurai JJ. 1985. Modern Quantum Mechanics. Menlo Park, CA: Benjamin/Cummings assumes that systems go to thermal equilibrium (thermalisation). The process of thermalisation erases local memory of the initial conditions. The eigenstate thermalisation hypothesis is a hypothesis about when quantum states will undergo thermalisation and why.
Not all quantum states undergo thermalisation. Some states have been discovered which do not (see below), and their reasons for not reaching thermal equilibrium are unclear {{As of|2019|March|lc=y}}.
Theoretical description
The process of equilibration can be described using the H-theorem or the relaxation theorem,{{Cite journal|last1=Reid|first1=James C.|last2=Evans|first2=Denis J.|last3=Searles|first3=Debra J.|date=2012-01-11|title=Communication: Beyond Boltzmann's H-theorem: Demonstration of the relaxation theorem for a non-monotonic approach to equilibrium|journal=The Journal of Chemical Physics|volume=136|issue=2|pages=021101|doi=10.1063/1.3675847|pmid=22260556|bibcode=2012JChPh.136b1101R |issn=0021-9606|url=https://espace.library.uq.edu.au/view/UQ:282860/UQ282860_OA.pdf|hdl=1885/16927|hdl-access=free}} see also entropy production.
Systems resisting thermalisation
= Classical systems =
Broadly-speaking, classical systems with non-chaotic behavior will not thermalise. Systems with many interacting constituents are generally expected to be chaotic, but this assumption sometimes fails. A notable counter example is the Fermi–Pasta–Ulam–Tsingou problem, which displays unexpected recurrence and will only thermalise over very long time scales.{{cite book | title=The Fermi-Pasta-Ulam Problem - A Status Report | series=Lecture Notes in Physics | publisher=Springer Berlin Heidelberg | publication-place=Berlin, Heidelberg | volume=728 | date=2008 | isbn=978-3-540-72994-5 | doi=10.1007/978-3-540-72995-2 | editor-last1=Gallavotti | editor-first1=Giovanni }} Non-chaotic systems which are pertubed by weak non-linearities will not thermalise for a set of initial conditions, with non-zero volume in the phase space, as stated by the KAM theorem, although the size of this set decreases exponentially with the number of degrees of freedom.{{cite book | last=Dumas | first=H. Scott | title=The KAM Story – A Friendly Introduction to the Content, History, and Significance of Classical Kolmogorov–Arnold–Moser Theory | publisher=World Scientific Publishing Company Incorporated | publication-place=[Hackensack], New Jersey | date=2014 | isbn=978-981-4556-58-3 | page=}} Many-body integrable systems, which have an extensive number of conserved quantities, will not thermalise in the usual sense, but will equilibrate according to a generalized Gibbs ensemble.{{cite journal | last1=Doyon | first1=Benjamin | last2=Hübner | first2=Friedrich | last3=Yoshimura | first3=Takato | title=New Classical Integrable Systems from Generalized TT-Deformations | journal=Physical Review Letters | volume=132 | issue=25 | date=2024-06-17 | issn=0031-9007 | doi=10.1103/PhysRevLett.132.251602 | page=251602| pmid=38996253 | arxiv=2311.06369 }}{{cite journal | last=Spohn | first=Herbert | title=Generalized Gibbs Ensembles of the Classical Toda Chain | journal=Journal of Statistical Physics | volume=180 | issue=1–6 | date=2020 | issn=0022-4715 | doi=10.1007/s10955-019-02320-5 | pages=4–22| arxiv=1902.07751 }}
= Quantum systems =
Some such phenomena resisting the tendency to thermalize include (see, e.g., a quantum scar):{{Cite web |date=March 20, 2019 |title=Quantum Scarring Appears to Defy Universe's Push for Disorder |url=https://www.quantamagazine.org/quantum-scarring-appears-to-defy-universes-push-for-disorder-20190320/ |access-date=March 24, 2019 |website=Quanta Magazine}}
- Conventional quantum scars,{{Cite journal |last=Heller |first=Eric J. |date=1984-10-15 |title=Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic Orbits |url=https://link.aps.org/doi/10.1103/PhysRevLett.53.1515 |journal=Physical Review Letters |volume=53 |issue=16 |pages=1515–1518 |doi=10.1103/PhysRevLett.53.1515|bibcode=1984PhRvL..53.1515H |url-access=subscription }}{{Cite journal |last=Kaplan |first=L |date=1999-01-01 |title=Scars in quantum chaotic wavefunctions |url=https://doi.org/10.1088/0951-7715/12/2/009 |journal=Nonlinearity |language=en |volume=12 |issue=2 |pages=R1–R40 |doi=10.1088/0951-7715/12/2/009 |s2cid=250793219 |issn=0951-7715|url-access=subscription |arxiv=chao-dyn/9810013 }}{{Cite journal |last1=Kaplan |first1=L. |last2=Heller |first2=E. J. |date=1998-04-10 |title=Linear and Nonlinear Theory of Eigenfunction Scars |url=https://www.sciencedirect.com/science/article/pii/S0003491697957730 |journal=Annals of Physics |language=en |volume=264 |issue=2 |pages=171–206 |doi=10.1006/aphy.1997.5773 |arxiv=chao-dyn/9809011 |bibcode=1998AnPhy.264..171K |s2cid=120635994 |issn=0003-4916}}{{Cite book |last=Heller |first=Eric |url=http://worldcat.org/oclc/1104876980 |title=The Semiclassical Way to Dynamics and Spectroscopy |date=5 June 2018 |publisher=Princeton University Press |isbn=978-1-4008-9029-3 |oclc=1104876980}} which refer to eigenstates with enhanced probability density along unstable periodic orbits much higher than one would intuitively predict from classical mechanics.
- Perturbation-induced quantum scarring:{{Cite journal |last1=Keski-Rahkonen |first1=J. |last2=Ruhanen |first2=A. |last3=Heller |first3=E. J. |last4=Räsänen |first4=E. |date=2019-11-21 |title=Quantum Lissajous Scars |url=https://link.aps.org/doi/10.1103/PhysRevLett.123.214101 |journal=Physical Review Letters |volume=123 |issue=21 |pages=214101 |doi=10.1103/PhysRevLett.123.214101|pmid=31809168 |arxiv=1911.09729 |bibcode=2019PhRvL.123u4101K |s2cid=208248295 }}{{Cite journal |last1=Luukko |first1=Perttu J. J. |last2=Drury |first2=Byron |last3=Klales |first3=Anna |last4=Kaplan |first4=Lev |last5=Heller |first5=Eric J. |last6=Räsänen |first6=Esa |date=2016-11-28 |title=Strong quantum scarring by local impurities |journal=Scientific Reports |language=en |volume=6 |issue=1 |pages=37656 |doi=10.1038/srep37656 |issn=2045-2322 |pmc=5124902 |pmid=27892510|arxiv=1511.04198 |bibcode=2016NatSR...637656L }}{{Cite journal |last1=Keski-Rahkonen |first1=J. |last2=Luukko |first2=P. J. J. |last3=Kaplan |first3=L. |last4=Heller |first4=E. J. |last5=Räsänen |first5=E. |date=2017-09-20 |title=Controllable quantum scars in semiconductor quantum dots |url=https://link.aps.org/doi/10.1103/PhysRevB.96.094204 |journal=Physical Review B |volume=96 |issue=9 |pages=094204 |doi=10.1103/PhysRevB.96.094204|arxiv=1710.00585 |bibcode=2017PhRvB..96i4204K |s2cid=119083672 }}{{Cite journal |last1=Keski-Rahkonen |first1=J |last2=Luukko |first2=P J J |last3=Åberg |first3=S |last4=Räsänen |first4=E |date=2019-01-21 |title=Effects of scarring on quantum chaos in disordered quantum wells |url=https://doi.org/10.1088/1361-648x/aaf9fb |journal=Journal of Physics: Condensed Matter |language=en |volume=31 |issue=10 |pages=105301 |doi=10.1088/1361-648x/aaf9fb |pmid=30566927 |arxiv=1806.02598 |bibcode=2019JPCM...31j5301K |s2cid=51693305 |issn=0953-8984}}{{Cite book |last=Keski-Rahkonen |first=Joonas |url=https://trepo.tuni.fi/handle/10024/123296 |title=Quantum Chaos in Disordered Two-Dimensional Nanostructures |date=2020 |publisher=Tampere University |isbn=978-952-03-1699-0 |language=en}} despite the similarity in appearance to conventional scarring, these scars have a novel underlying mechanism stemming from the combined effect of nearly-degenerate states and spatially localized perturbations, and they can be employed to propagate quantum wave packets in a disordered quantum dot with high fidelity.
- Many-body quantum scars.
- Many-body localisation (MBL),{{Cite journal |doi = 10.1146/annurev-conmatphys-031214-014726|title = Many-Body Localization and Thermalization in Quantum Statistical Mechanics|journal = Annual Review of Condensed Matter Physics|volume = 6|pages = 15–38|year = 2015|last1 = Nandkishore|first1 = Rahul|last2 = Huse|first2 = David A.|last3 = Abanin|first3 = D. A.|last4 = Serbyn|first4 = M.|last5 = Papić|first5 = Z.|bibcode = 2015ARCMP...6...15N|arxiv = 1404.0686|s2cid = 118465889}} quantum many-body systems retaining memory of their initial condition in local observables for arbitrary amounts of time.{{Cite journal |doi = 10.1126/science.aaf8834|pmid = 27339981|title = Exploring the many-body localization transition in two dimensions|journal = Science|volume = 352|issue = 6293|pages = 1547–1552|year = 2016|last1 = Choi|first1 = J.-y.|last2 = Hild|first2 = S.|last3 = Zeiher|first3 = J.|last4 = Schauss|first4 = P.|last5 = Rubio-Abadal|first5 = A.|last6 = Yefsah|first6 = T.|last7 = Khemani|first7 = V.|last8 = Huse|first8 = D. A.|last9 = Bloch|first9 = I.|last10 = Gross|first10 = C.|bibcode = 2016Sci...352.1547C|arxiv = 1604.04178|s2cid = 35012132}}{{Cite journal |doi = 10.1103/PhysRevLett.120.070501|pmid = 29542978|title = Exploring Localization in Nuclear Spin Chains|journal = Physical Review Letters|volume = 120|issue = 7|pages = 070501|year = 2018|last1 = Wei|first1 = Ken Xuan|last2 = Ramanathan|first2 = Chandrasekhar|last3 = Cappellaro|first3 = Paola|bibcode = 2018PhRvL.120g0501W|arxiv = 1612.05249|s2cid = 4005098}}
Other systems that resist thermalisation and are better understood are quantum integrable systems{{Cite journal|last1=Caux|first1=Jean-Sébastien|last2=Essler|first2=Fabian H. L.|date=2013-06-18|title=Time Evolution of Local Observables After Quenching to an Integrable Model|journal=Physical Review Letters|volume=110|issue=25|pages=257203|doi=10.1103/PhysRevLett.110.257203|pmid=23829756|s2cid=3549427|doi-access=free|arxiv=1301.3806|bibcode=2013PhRvL.110y7203C }} and systems with dynamical symmetries.{{Cite journal|last1=Buča|first1=Berislav|last2=Tindall|first2=Joseph|last3=Jaksch|first3=Dieter|date=2019-04-15|title=Non-stationary coherent quantum many-body dynamics through dissipation|url= |journal=Nature Communications|language=en|volume=10|issue=1|pages=1730|doi=10.1038/s41467-019-09757-y|issn=2041-1723|pmc=6465298|pmid=30988312|arxiv=1804.06744 |bibcode=2019NatCo..10.1730B }}